The invention relates generally to processing of numerical data which characterize subsurface earth formations. More particularly, the invention relates to a method and a system for optimizing the injection and production well fluid allocation factors used in a material balance analysis of a hydrocarbon reservoir.
In the commercial recovery of hydrocarbons it is desirable to estimate the fluid saturations and pressure changes that occur in the reservoir as a result of injecting fluids into the reservoir and producing fluids therefrom, and then compare these results with actual measurements to maximize the efficiency of recovery. A key constraint in determining accurate estimates is the conservation of total mass of injected and produced fluids, i.e., the "material balance."
As used in the art, the term "material balance" describes the process of determining the total fluid volumes entering and leaving a volume over a time period using this information to compute resulting reservoir pressures and fluid saturations. Material balance calculations are well known and described fully in Petroleum Reservoir Engineering: Physical Properties, J. W. Amyx, D. M. Bass, Jr., R. L. Whiting, McGraw-Hill Book Co., New York, 1960, pp. 561-598, and Applied Petroleum Reservoir Engineering, B. C. Craft and M. F. Hawkins, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1959, pp 148-156 (hereinafter collectively referred to as "Material Balance References"). Generally, the reservoir is divided into a set of volumes called "Patterns" centered on producing wells with injection wells on the pattern borders. A separate material balance calculation is performed for each pattern. Because injection wells are on pattern boundaries, fluid from a single injection well must be allocated to more than one pattern. Current practice is to estimate the allocation of fluids from each of the injection wells surrounding a producer by assigning allocation factors for each well, where the allocation factors represent the fraction of fluid injected to or produced from a well, into or out of a well pattern. For production wells, the production allocation factors describe the split of produced fluids among production zones vertically (e.g., two production zones would result in two unknown allocation factors for each production well). Injection well allocation factors describe the portion of injected fluid that migrates to each of the surrounding production wells for each production zone. For example, an injection well completed in two production zones and bordering on four patterns will result in eight unknown allocation factors.
Mathematical solution of the fluid allocation problem is complex because, for a typical reservoir, there can be hundreds to thousands of unknown allocation factors. Reservoir pressure response to injection and production is non-linear making the allocation factors difficult to estimate by traditional optimization techniques. When comparing estimates to actual data, changing a well allocation in one pattern to match field observations changes the well allocation factors in all surrounding patterns. Traditional practice is to manually iterate possible solutions for the allocation of fluids from each of the injection wells surrounding a producer until a "reasonable" pressure profile for all patterns in the reservoir is achieved. This is a labor intensive and subjective process. Efforts to automate this allocation process using a least-squares, linear programming approach have not been satisfactory.
By way of further background, optimization methods known as "genetic algorithms" have been applied to non-linear problems in many diverse areas, including operation of a gas pipeline, factory scheduling and semiconductor layout. Genetic algorithms serve to select a string (referred to as a "chromosome") of numbers ("genes") having values ("alleles") that provides the optimum value of a "fitness function." According to this technique, a group of chromosomes (a "generation") is first randomly generated, and the fitness function is evaluated for each chromosome. A probability function is then produced to assign a probability value to each of the chromosomes according to its fitness function value, so that a chromosome with a higher fitness function value obtains a higher probability. A "reproduction pool" of chromosomes is then produced by random selection according to the probability function; the members of this reproduction pool are more likely to be selected from the higher fitness function values. A randomly selected chromosome from the reproduction pool then "reproduces" with another, randomly selected, chromosome in the reproduction pool by exchange of genes at a randomly selected "crossover" point in the chromosome. This reproduction is repeated to generate a second generation of chromosomes. Mutation may be introduced by randomly altering a small fraction of the genes in the second generation (e.g., one in one thousand). The fitness function is then evaluated for each of the chromosomes in the second generation, and the reproduction process is repeated until the desired convergence is obtained.
What is needed, therefore, is a method of automating the material balance process as it relates to the estimate of fluid allocation factors for production and injection wells in the reservoir, using a stochastic optimization technique, such as a genetic algorithm procedure, that can more readily accommodate non-linear aspects of this problem. cl SUMMARY OF THE INVENTION
The present invention, accordingly, provides a system and method of producing a material balance solution for well patterns in a hydrocarbon reservoir that automatically optimizes the fluid allocation factors for each well used in determining the solution. The system and method is applied to a hydrocarbon reservoir having injection and production wells in which well patterns are defined volumes centered around each production well with fluid contributions from injection wells at the pattern boundaries. The allocation factors represent the fraction of fluid injected to or produced from a well into or out of a well pattern.
In one embodiment, the system and method automatically optimizes estimates for the allocation factors to be used in the material balance solution by randomly generating a first generation of allocation factor strings, each string in the generation assigning allocation factors to each of the wells in the reservoir. A fitness function value is determined for each of the strings by evaluating a fitness function, wherein the fitness function comprises the sum of the differences between computed and measured field pressures for each pattern, and the sum of the differences between target allocation factors and the allocation factors specified within the string for each well. A succeeding generation of allocation factor strings is produced according to a genetic algorithm. The process of determining a fitness function value for each of the strings is then repeated for the succeeding generation. The string having fitness function value meeting a specified criteria is identified, wherein the identified string includes optimized estimates of the allocation factors for the reservoir for use in determining the material balance solution.
In another aspect, the identification of the fitness function value meeting the criteria further includes determining whether the criteria has been satisfied, whereupon the string identification occurs when the criteria has been satisfied; and further, responsive to determining that the predetermined criteria is not satisfied, repeating the steps of producing a succeeding generation of strings; and determining a fitness function value for each of the strings in the succeeding generation.
In another aspect of the invention, the process of producing a succeeding generation of allocation factor strings comprises creating a probability value for each of the allocation factor strings in first generation by determining the fractional contribution of each string in the generation to the sum of the fitness function values for the strings in the generation; selecting parent sequences from the first generation according to the probability values; randomly selecting pairs of parent strings; and crossing over the selected pairs of parent strings relative to one another at a randomly selected value position to produce the succeeding generation.
In a preferred embodiment the invention is implemented as computer program instructions stored on computer-readable media. The program can run on any PC or workstation.
A technical advantage achieved with the invention is accuracy in estimating allocation factors needed in developing a material balance solution heretofore not readily obtainable with traditional estimation techniques. A result of the foregoing is a material balance solution that enables hydrocarbons to be more efficiently swept from a reservoir.
Another technical advantage achieved is a substantial reduction in manpower and saving of time normally required to determine estimates of allocation factors for well production and injection in large reservoirs. dr